基于跳跃CKLS模型对我国利率期限结构的研究

发布时间：2018-03-05 09:02

本文选题：跳跃CKLS模型　切入点：Euler法　出处：《浙江工商大学》2014年硕士论文　论文类型：学位论文

【摘要】：利率作为金融市场中资产定价、金融产品设计、利率风险管理等研究的重要理论基础,其在金融市场中占着非常重要的地位。近年来,国际金融市场中对利率期限结构模型的研究亦是愈演愈烈,因此本文对利率期限结构模型理论进行了扩展分析及实证估计。本文以CKLS模型作为研究对象,考虑了市场中一些突发状况的发生对利率产生的影响以及实际利率具有尖峰厚尾性等特征,从而在CKLS模型中引入跳跃项,并且分别估算出不同情形下跳跃CKLS模型的转移密度函数,最后则用MCMC参数估计方法进行了实证分析,并得到各个参数序列的统计值以及参数估计过程中的核密度图等,以便分析中国利率市场的基本特征,具体如下。首先,建立利率期限结构模型。文章先后对比了目前理论上几种重要的利率期限结构模型,最终选择了CKLS模型作为本文的研究对象,并结合中国利率市场的特点,在模型中加入了跳跃因子。关于跳跃部分,本文分两种情形进行了分析,一是在规定时间间隔内至多发生一次跳；二是在规定时间间隔内可能发生多次跳跃,且假设发生跳跃的次数服从泊松过程。其次,求解模型转移密度。由于本文中所用模型比较复杂,无法求出模型转移密度函数的数值解,因此本文采用离散化的方法估算出了模型的转移密度函数,也可理解为条件密度函数。在离散化方法的选择中,本文选用了既简单又容易实施的Euler离散化方法。这一部分所求得的密度函数则为接下来的MCMC参数估计中似然函数的求解打下了重要的基础。最后,参数估计及实证分析。在参数估计的方法选择方面,本文采用的是基于贝叶斯原理的MCMC方法,利用MCMC方法经过多次模拟得到各项参数的基本统计特征值、核密度图形以及分位数图形等,最终选取多次模拟结果的均值作为参数的估计值。在数据选择方面,本文结合了中国利率市场的特点,分析了上海银行间同业拆放利率各个品种的交易量及相互之间的相关性等特征,最终选取了上海银行间同业拆放隔夜利率作为金融市场利率的一个替代。在参数估计过程中,本文对基于Euler离散化方法下求出的似然函数运用MCMC方法做出了模拟,并利用所得到的结果作为分析对象,对实证结果进行了分析。
[Abstract]:Interest rate, as an important theoretical basis of asset pricing, financial product design and interest rate risk management in financial market, occupies a very important position in financial market in recent years. The research on term structure model of interest rate in international financial market is becoming more and more serious, so this paper makes an extended analysis and empirical estimation on the theory of term structure model of interest rate. In this paper, the CKLS model is taken as the research object, considering the influence of some unexpected situations on the interest rate in the market, and the real interest rate has the characteristics of peak and thick tail, so the jump term is introduced into the CKLS model. The transfer density function of the hopping CKLS model is estimated in different cases. Finally, the empirical analysis is carried out by using the MCMC parameter estimation method, and the statistical values of each parameter sequence and the kernel density graph in the process of parameter estimation are obtained. In order to analyze the basic characteristics of China's interest rate market, as follows. First of all, the paper establishes the term structure model of interest rate. This paper compares several important term structure models of interest rate in theory, and finally chooses CKLS model as the research object of this paper, and combines the characteristics of interest rate market in China. The jump factor is added to the model. As for the jump part, this paper analyzes it in two cases: one is that there is at most one jump within the specified time interval, the other is that multiple jumps may occur in the specified time interval. And assume that the number of jumps occurs from the Poisson process. Secondly, the transfer density of the model is solved. Because the model used in this paper is very complicated, the numerical solution of the transfer density function of the model can not be obtained, so the transfer density function of the model is estimated by the discrete method. It can also be understood as conditional density function. In the selection of discretization methods, In this paper, the Euler discretization method, which is simple and easy to implement, is chosen. The density function obtained in this part lays an important foundation for the solution of the likelihood function in the next MCMC parameter estimation. Finally, the parameter estimation and empirical analysis. In the method selection of parameter estimation, this paper adopts the MCMC method based on Bayesian principle, and obtains the basic statistical characteristic value of each parameter by MCMC method after many times simulation. The kernel density graph and the quantile graph are used to select the mean value of multiple simulation results as the estimated value of the parameters. In terms of data selection, this paper combines the characteristics of the interest rate market in China. Based on the analysis of the transaction volume and the correlation among the various kinds of Shanghai interbank offered rate, the overnight interest rate of Shanghai interbank offered rate is selected as an alternative to the interest rate in the financial market. In the process of parameter estimation, In this paper, the likelihood function based on Euler discretization method is simulated by MCMC method, and the empirical results are analyzed by using the obtained results as the object of analysis.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.5;F224

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